Given 100 nuts in five paper bags, in the first and second bags there
are altogether fifty-two nuts; in the second and third there are
forty-three; in the third and fourth, thirty-four; in the fourth and
fifth, thirty. How many nuts are there in each bag?

A young entrepreneur struggles to reverse-engineer the mark-up price that
guarantees his take-home profit. Starting with his own steps as a framework, Doctor
Peterson introduces variables and applies algebra to model the scenario more
generally.

The sum of 1/2, 1/3, and 1/4 of the enrollment of the Business School
is exactly the enrollment of the Language School. The sum of 1/5, 1/6,
1/7, and 1/8 of the enrollment of the Business School is exactly that
of the Design School. What are the enrollments of these three schools,
assuming no school has more than 1000 pupils?

A student struggles with an algebra word problem. Doctor Ian breaks it down into
manageable chunks, stepping through how to represent the question's relationships
algebraically and then check his interpretation for reasonableness.

A handcar sets out from Chicago to Detroit at an average speed of 10mph.
Four hours later a freight train starts a run from Detroit to Chicago at
an average speed of 20 mph. Assuming the rail distance between the two
cities is 400 miles, which will be closer to Chicago when they meet?

You must spend $100 to buy 100 pets, choosing at least one of each
pet. The pets and their prices are: mice @ $0.25 each, cats @ $1.00
each, and dogs @ $15.00 each. How many mice, cats, and dogs must you
buy?